My teacher said "Keep in mind that g is a positive number. It is tempting to substitute -9.80m/s² for g. Downward acceleration is indicated explicitly by stating the acceleration ay = -g"
In our homework, I encountered where his statement was true, but I don't understand why.
Ex1.A ball is thrown directly downward with an initial speed of 7.35 m/s from a height of 30.6 m. After what time interval does it strike the ground?
I know that acceleration is constant because of gravity, so i can use the formula d = (v + v₀)t/2 or d = v₀t + ½at² + d₀
But when I used either formula as I tried to find the final velocity
30.6 = (v - 7.35)t/2
v² = (-7.35)² + 2(-9.8)(30.6)
v² = -545.7375
So now I can't use d = (v + v₀)t/2.
When I used d = -4.9t² - 7.35t + 30.6, I get t = 1.85s
Now I really want to know why the other formula did not work and why must I use a positive 9.8m/s²? Please explain
Update:Is it because gravity is always a vector pointing down?
Answers & Comments
Verified answer
Standard gravity is specified by SI standards as a positive number, namely 9.80665 m/s^2, though it's actually written as g with a small n subscript. The reason the standard gravity is defined as positive is because it's used to compute the standard weight of an object based on its mass. You wouldn't want the weight coming out negative.
If you're using it in a problem, though, you have to consider the direction of gravity relative to your coordinate system.
Acceleration due to gravity (g) is positive or negative based on the direction. When you throw an object in the air, the velocity is directed upwards. To slow the ball down, gravity acts as a negative acceleration so the ball can go in the opposite direction. When you drop an object from an initial point, the acceleration due to gravity would be positive because the velocity is increasing in the same direction it was going when it started. When the object slows down when it is thrown upwards into the air, the gravity acts as a negative acceleration. When the object speeds up when it is dropped, it is a positive acceleration.
Hope this helps!
EDIT: It depends on the initial direction of the velocity. If the velocity is pointing up (the object is thrown in the air), gravity will act as a negative acceleration so the velocity will go in the opposite direction from where it came originally. If the velocity is pointing down (the object is dropped), gravity will act as a positive accleration because the velocity and the accleration are going in the same direction.
You are free to choose your own sign convention. Up is not always positive and down is not always negative....EVERY PROBLEM IS DIFFERENT.
g is a vector. It always points down. If used as a simple number, g refers to the MAGNITUDE of the gravitational field...not both magnitude and direction.